Congressional Republicans warned Mr. Obama last year against moving political appointees into career positions, and President Trump has stated frequently that he believes some employees in the federal workforce are Obama holdovers working against his agenda.

The practice of political appointees “burrowing” into career jobs is permissible when laws and regulations governing career appointments are followed. Administrations prior to the Obama administration also have converted dozens of political appointees into career government jobs.

Sen. John Thune, South Dakota Republican, said he requested the GAO report in part “to make sure executive branch employees knew they were being watched for improper burrowing.”

“Still, GAO determined that one out of every five attempts to move a political appointee into a career position was rejected as improper,” Mr. Thune said. “Watchdogs need to stay vigilant, and I intend to seek more information about the individuals who may have led improper hiring initiatives.”

The Department of Homeland Security had the highest number of conversions, (nine), followed by the Department of Justice (eight).

Defense had six. Treasury had five. Agriculture, Commerce, Health and Human Services and the Federal Deposit Insurance Corp. each had four.

Three of the unapproved cases involved people in posts at the Education Department (a program specialist), at the Department of Health and Human Services (a senior adviser) and at the Federal Deposit Insurance Corp. (a legislative adviser), according to a source briefed in advance on GAO’s review. In all three cases, agencies submitted materials on the conversion cases to OPM for post-appointment reviews.

The GAO report found that OPM approved 78 of 99 requests to convert political appointees to career positions from Jan. 1, 2010, through March 17, 2016. OPM denied 21 requests for varying reasons, such as bypassing qualified veterans, and referred nine denied cases to the Office of Special Counsel.

Of the 78 approved requests, agencies followed through and converted 69 political appointees to career positions.

The practice of burrowing has been going on decades, although the vast majority of an administration’s approximately 4,000 political appointees leave office with a change in presidents.

The George W. Bush administration allowed 135 political appointees to convert to career jobs from January 2001 to June 2008. An Associated Press investigation found at least 26 such cases approved during Mr. Bush’s final year in office.

A Congressional Research Service report last year said burrowing frequently occurs during the transition period when one administration is preparing to leave office and a new administration is coming in. CRS said the practice can foster the belief that “the individual who is converted to a career position may seek to undermine the work of the new administration whose policies may be at odds with those that he or she espoused when serving in the appointed capacity.”

The GAO report said of the 78 OPM-approved agency requests from 2010 to 2016, agencies “appeared to have used appropriate authorities and followed proper procedures in converting political appointees to career positions.”

“More specifically, for each of the 78 cases, our review of OPM’s case files and additional documentation from individual agencies supported OPM’s conclusion that each of these conversions appeared to be free of political influence,” the report said.